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Java example source code file (LegendreHighPrecisionRuleFactory.java)

This example Java source code file (LegendreHighPrecisionRuleFactory.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

baserulefactory, bigdecimal, dimensionmismatchexception, legendrehighprecisionrulefactory, math, mathcontext, override, pair

The LegendreHighPrecisionRuleFactory.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.analysis.integration.gauss;

import java.math.BigDecimal;
import java.math.MathContext;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.util.Pair;

/**
 * Factory that creates Gauss-type quadrature rule using Legendre polynomials.
 * In this implementation, the lower and upper bounds of the natural interval
 * of integration are -1 and 1, respectively.
 * The Legendre polynomials are evaluated using the recurrence relation
 * presented in <a href="http://en.wikipedia.org/wiki/Abramowitz_and_Stegun">
 * Abramowitz and Stegun, 1964</a>.
 *
 * @since 3.1
 */
public class LegendreHighPrecisionRuleFactory extends BaseRuleFactory<BigDecimal> {
    /** Settings for enhanced precision computations. */
    private final MathContext mContext;
    /** The number {@code 2}. */
    private final BigDecimal two;
    /** The number {@code -1}. */
    private final BigDecimal minusOne;
    /** The number {@code 0.5}. */
    private final BigDecimal oneHalf;

    /**
     * Default precision is {@link MathContext#DECIMAL128 DECIMAL128}.
     */
    public LegendreHighPrecisionRuleFactory() {
        this(MathContext.DECIMAL128);
    }

    /**
     * @param mContext Precision setting for computing the quadrature rules.
     */
    public LegendreHighPrecisionRuleFactory(MathContext mContext) {
        this.mContext = mContext;
        two = new BigDecimal("2", mContext);
        minusOne = new BigDecimal("-1", mContext);
        oneHalf = new BigDecimal("0.5", mContext);
    }

    /** {@inheritDoc} */
    @Override
    protected Pair<BigDecimal[], BigDecimal[]> computeRule(int numberOfPoints)
        throws DimensionMismatchException {

        if (numberOfPoints == 1) {
            // Break recursion.
            return new Pair<BigDecimal[], BigDecimal[]>(new BigDecimal[] { BigDecimal.ZERO },
                                                        new BigDecimal[] { two });
        }

        // Get previous rule.
        // If it has not been computed yet it will trigger a recursive call
        // to this method.
        final BigDecimal[] previousPoints = getRuleInternal(numberOfPoints - 1).getFirst();

        // Compute next rule.
        final BigDecimal[] points = new BigDecimal[numberOfPoints];
        final BigDecimal[] weights = new BigDecimal[numberOfPoints];

        // Find i-th root of P[n+1] by bracketing.
        final int iMax = numberOfPoints / 2;
        for (int i = 0; i < iMax; i++) {
            // Lower-bound of the interval.
            BigDecimal a = (i == 0) ? minusOne : previousPoints[i - 1];
            // Upper-bound of the interval.
            BigDecimal b = (iMax == 1) ? BigDecimal.ONE : previousPoints[i];
            // P[j-1](a)
            BigDecimal pma = BigDecimal.ONE;
            // P[j](a)
            BigDecimal pa = a;
            // P[j-1](b)
            BigDecimal pmb = BigDecimal.ONE;
            // P[j](b)
            BigDecimal pb = b;
            for (int j = 1; j < numberOfPoints; j++) {
                final BigDecimal b_two_j_p_1 = new BigDecimal(2 * j + 1, mContext);
                final BigDecimal b_j = new BigDecimal(j, mContext);
                final BigDecimal b_j_p_1 = new BigDecimal(j + 1, mContext);

                // Compute P[j+1](a)
                // ppa = ((2 * j + 1) * a * pa - j * pma) / (j + 1);

                BigDecimal tmp1 = a.multiply(b_two_j_p_1, mContext);
                tmp1 = pa.multiply(tmp1, mContext);
                BigDecimal tmp2 = pma.multiply(b_j, mContext);
                // P[j+1](a)
                BigDecimal ppa = tmp1.subtract(tmp2, mContext);
                ppa = ppa.divide(b_j_p_1, mContext);

                // Compute P[j+1](b)
                // ppb = ((2 * j + 1) * b * pb - j * pmb) / (j + 1);

                tmp1 = b.multiply(b_two_j_p_1, mContext);
                tmp1 = pb.multiply(tmp1, mContext);
                tmp2 = pmb.multiply(b_j, mContext);
                // P[j+1](b)
                BigDecimal ppb = tmp1.subtract(tmp2, mContext);
                ppb = ppb.divide(b_j_p_1, mContext);

                pma = pa;
                pa = ppa;
                pmb = pb;
                pb = ppb;
            }
            // Now pa = P[n+1](a), and pma = P[n](a). Same holds for b.
            // Middle of the interval.
            BigDecimal c = a.add(b, mContext).multiply(oneHalf, mContext);
            // P[j-1](c)
            BigDecimal pmc = BigDecimal.ONE;
            // P[j](c)
            BigDecimal pc = c;
            boolean done = false;
            while (!done) {
                BigDecimal tmp1 = b.subtract(a, mContext);
                BigDecimal tmp2 = c.ulp().multiply(BigDecimal.TEN, mContext);
                done = tmp1.compareTo(tmp2) <= 0;
                pmc = BigDecimal.ONE;
                pc = c;
                for (int j = 1; j < numberOfPoints; j++) {
                    final BigDecimal b_two_j_p_1 = new BigDecimal(2 * j + 1, mContext);
                    final BigDecimal b_j = new BigDecimal(j, mContext);
                    final BigDecimal b_j_p_1 = new BigDecimal(j + 1, mContext);

                    // Compute P[j+1](c)
                    tmp1 = c.multiply(b_two_j_p_1, mContext);
                    tmp1 = pc.multiply(tmp1, mContext);
                    tmp2 = pmc.multiply(b_j, mContext);
                    // P[j+1](c)
                    BigDecimal ppc = tmp1.subtract(tmp2, mContext);
                    ppc = ppc.divide(b_j_p_1, mContext);

                    pmc = pc;
                    pc = ppc;
                }
                // Now pc = P[n+1](c) and pmc = P[n](c).
                if (!done) {
                    if (pa.signum() * pc.signum() <= 0) {
                        b = c;
                        pmb = pmc;
                        pb = pc;
                    } else {
                        a = c;
                        pma = pmc;
                        pa = pc;
                    }
                    c = a.add(b, mContext).multiply(oneHalf, mContext);
                }
            }
            final BigDecimal nP = new BigDecimal(numberOfPoints, mContext);
            BigDecimal tmp1 = pmc.subtract(c.multiply(pc, mContext), mContext);
            tmp1 = tmp1.multiply(nP);
            tmp1 = tmp1.pow(2, mContext);
            BigDecimal tmp2 = c.pow(2, mContext);
            tmp2 = BigDecimal.ONE.subtract(tmp2, mContext);
            tmp2 = tmp2.multiply(two, mContext);
            tmp2 = tmp2.divide(tmp1, mContext);

            points[i] = c;
            weights[i] = tmp2;

            final int idx = numberOfPoints - i - 1;
            points[idx] = c.negate(mContext);
            weights[idx] = tmp2;
        }
        // If "numberOfPoints" is odd, 0 is a root.
        // Note: as written, the test for oddness will work for negative
        // integers too (although it is not necessary here), preventing
        // a FindBugs warning.
        if (numberOfPoints % 2 != 0) {
            BigDecimal pmc = BigDecimal.ONE;
            for (int j = 1; j < numberOfPoints; j += 2) {
                final BigDecimal b_j = new BigDecimal(j, mContext);
                final BigDecimal b_j_p_1 = new BigDecimal(j + 1, mContext);

                // pmc = -j * pmc / (j + 1);
                pmc = pmc.multiply(b_j, mContext);
                pmc = pmc.divide(b_j_p_1, mContext);
                pmc = pmc.negate(mContext);
            }

            // 2 / pow(numberOfPoints * pmc, 2);
            final BigDecimal nP = new BigDecimal(numberOfPoints, mContext);
            BigDecimal tmp1 = pmc.multiply(nP, mContext);
            tmp1 = tmp1.pow(2, mContext);
            BigDecimal tmp2 = two.divide(tmp1, mContext);

            points[iMax] = BigDecimal.ZERO;
            weights[iMax] = tmp2;
        }

        return new Pair<BigDecimal[], BigDecimal[]>(points, weights);
    }
}

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